Question

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Answer 1

Below in bold.

Explanation:

1) ( a^2 + b^2 = (a + b)^2 - 2ab

= 29 - 2(6)

= 29-12

= 17.

2). (x - y)^2 = x^2 + y^2 - 2xy

so 20 = 18 - 2xy

2xy = 18-20 = -2

xy = -1.

3). 1/x + x = 7

(1/ x + x)^2 = 1/x^2 + x^2 +x/x + x/x

= 1/x^2 + x^2 + 2

But(1/x + x)^2 = 7^2 = 49

so 1/x^2 + x^2 + 2 = 49

so 1/x^2 + x^2 = 49 - 2 = 47.